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Given an undirected graph with edge costs and a subset of k ≥ 3 nodes called terminals, a multiway, or k-way, cut is a subset of the edges whose removal disconnects each terminal from the others. The multiway cut problem is to find a minimum-cost multiway cut. This problem is Max-SNP hard. Recently Calinescu, Karloff, and Rabani (STOC'98) gave a novel… (More)

Given a directed graph G = (V; E), a natural problem is to choose a minimum number of the edges in E such that, for any two vertices u and v, if there is a path from u to v in E, then there is a path from u to v among the chosen edges. We show that in graphs having no directed cycle with more than three edges, this problem is equivalent to Maximum Bipartite… (More)

1 Introduction

We describe sequential and parallel algorithms that approximately solve linear programs with no negative coefficients (a.k.a. mixed packing and covering problems). For explicitly given problems, our fastest sequential algorithm returns a solution satisfying all constraints within a 1 ± ǫ factor in O(md log(m)/ǫ 2) time, where m is the number of constraints… (More)

The paging problem is that of deciding which pages to keep in a memory of k pages in order to minimize the number of page faults. We develop the marking algorithm, a randomized on-line algorithm for the paging problem. We prove that its expected cost on any sequence of requests is within a factor of 2H k of optimum. (Where H k is the kth harmonic number,… (More)

We introduce a new technique called oblivious rounding | a variant of randomized rounding that avoids the bottleneck of rst solving the linear program. Avoiding this bottleneck yields more eecient algorithms and brings probabilistic methods to bear on a new class of problems. We give oblivious rounding algorithms that approximately solve general packing and… (More)

Efficient algorithms are known for computing a minimum spann.ing tree, or a shortest path. tree (with a fixed vertex as the root). The weight of a shortest path tree can be much more than the weight of a minimum spa,n-ning tree. Conversely, the distance bet,ween the root, and any vertex in a minimum spanning tree may be much more than the distance bet#ween… (More)

Time series shapelets are small, local patterns in a time series that are highly predictive of a class and are thus very useful features for building classifiers and for certain visualization and summarization tasks. While shapelets were introduced only recently, they have already seen significant adoption and extension in the community. Despite their… (More)

We give a simple algorithm to find a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous tradeoff: given the two trees and a 7 > 0, the algorithm returns a spanning tree in which the distance between any vertex and the root of the shortest-path tree is at most 1 + x/27 times… (More)

Given n points in the plane, the degree-K spanning tree problem asks for a spanning tree of minimum weight in which the degree of each vertex is at most K. This paper addresses the problem of computing low-weight degree-K spanning trees for K > 2. It is shown that for an arbitrary collection of n points in the plane, there exists a spanning tree of degree… (More)